Twin Paradox: Einstein's Explanation and Alternative Interpretations

[atyy]

If pointing out that in paragraph 3, chapter 4, of his article 'On the Electrodynamics of Moving Bodies' Albert Einstein wrote "A balance-clock at the equator must go more slowly than a precisely similar clock at one of the poles under otherwise identical conditions." is arguing "the validity of the mainstream understanding of relativity" then so be it.

The balance clock does go more slowly on average over a full rotation, and it also goes more slowly at every moment in the frame of the Earth, and as I said it is plausible that Einstein might have meant either of these. It's not correct that it's going more slowly at every moment in any objective physical sense though.

Given the analogy, I suggest that if the answer is "no" for the second scenario, it must also be "no" for the first scenario. If so, then we can ask if it makes any sense to say that "time" goes more slowly for B. If it is to make sense, then "time" in that statement cannot be "real time".

George Jones's post #8 has a rate of change of the proper time of one observer with respect to proper time of another observer (due to gravitational time dilation). What is the equivalent of this in the twin paradox? https://www.physicsforums.com/showthread.php?p=1543402

 

[atyy]

"In other words, Terence computes that Stella's clock is really running slow by a factor of about 7 the whole time, but he sees it running fast during the Inbound Leg because each flash has a shorter distance to travel."
http://www.math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_doppler.html

I like the picture with the red lines:
http://www.math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_vase.html

 

[JesseM]

George Jones's post #8 has a rate of change of the proper time of one observer with respect to proper time of another observer (due to gravitational time dilation). What is the equivalent of this in the twin paradox? https://www.physicsforums.com/showthread.php?p=1543402

George Jones' post wasn't comparing the rate of change of each observer's clock in any coordinate-invariant sense though--he specified that he was using Schwarzschild coordinates.

 

[phyti]

According to Einstein's chapter 4, STR, if clock A moves in any polygonal line to B's location (in the same way that the astronaut makes an out-and-return journey) clock A will "lag behind" clock B.

Einstein's equation refers to t which is the total elapsed time for each of the trips so although their clocks will be ticking over at the same rate as each other during those flights (based on v being identical) the amount by which Z's clock lags behind the clocks in San Francisco will be greater than the amount by which Y's clock lags behind those clocks.

If Y and Z have the same speed for the duration of their trips, and they leave and arrive together, their clocks read the same. A difference in clock time would imply one traveled a greater distance before reuniting, which implies a faster speed, which slows clock rate.

 

[cos]

OK, let me try state my question more clearly.

As a preliminary, the twins are Earth-bound A and astronaut B. Although A stays at the same "place", he moves through "time", and so moves through spacetime. Here's the analogy:

In the twin paradox, A and B start off at the same point in spacetime, then both of them move through spacetime in different paths, eventually meeting at another point in spacetime. At that point, they find that they have accumulated different amounts of ageing or real time. Does this mean that the "real time" between ticks of B's clock were greater?

Greater than the “real time” between ticks of A’s clock? Yes.

Before I go into details I again point out that my presentation is specifically in relation to Albert Einstein’s chapter 4 of his 1905 article ‘On the Electrodynamics of Moving Bodies’ depiction.

I have been accused of arguing the validity of the mainstream understanding of relativity however I fail to see why my referring to chapter 4 of relativity could be arguing that mainstream understanding of relativity.

It seems to me that some people are attempting to pretend that chapter 4 of special theory does not exist. If chapter 4 of relativity argues the validity of the mainstream understanding of relativity then I suggest that people should look at chapter 4. It is part and parcel of relativity thus should not be ignored even it is uncomfortable or inconvenient.

In that chapter (paragraph 1) Einstein wrote:- “If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by .5tv²/c² ... t being the time occupied in the journey from A to B.”

In paragraph 3 Einstein refers to a clock that has remained at rest compared with an identical clock that has moved in a closed curve around that clock. I am of the opinion that he implied that clock B in paragraph 1 remains at rest ergo, in that chapter, Einstein does not allow that clock B “moves through spacetime”.

If someone were to draw a diagram of clocks A and B moving through spacetime they would be presenting that phenomenon from the point of view of another reference frame however Einstein specifically pointed out that the event is “viewed in the stationary system” (i.e. clock B’s reference frame).

Although Einstein made no mention of the fact - it is obvious that clock A in paragraph 1 must accelerate in order to move to B’s location. On the basis that the attainment of an instantaneous velocity can be mathematically ‘ratified’ I can only repeat Einstein’s comment that as far as the propositions of mathematics are certain, they do not refer to reality and as far as I am concerned physics should be a study of physical reality thus Einstein’s paragraph 1, chapter 4, clock A must accelerate and as Einstein showed in his 1918 Naturwissenschaften article, it is only the clock that experiences forces of acceleration (clock A) that incurs variations in it’s rates of operation not the clock referred to in his 1918 article which continues to move with uniform velocity (clock B).

In paragraph 3, chapter 4, Einstein wrote:- “Thence we conclude that a balance clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles...”

My interpretation of the phase ‘must go more slowly’ is that the equatorial clock ticks over at a slower rate than (i.e. that it incurs time dilation relatively to) the polar clock.

On the basis that the equatorial clock ‘must go more slowly’ than the polar clock then it must progressively lag further and further behind the polar clock.

I interpret Einstein’s paragraph 1 conclusion that A will lag behind B as being in accordance with his later comment that A (his paragraph 3 equatorial clock) ‘goes more slowly’ (i.e. ticks over at a slower rate) than B (his paragraph 3 polar clock).

I am of the opinion that if Einstein’s paragraph 1 clock A was not located some distance away from B but was initially stationary alongside and synchronous with B then traveled away from B at the same velocity (v) and for the same length of time (t) as does Einstein’s clock A then comes to a stop it will then lag behind B by the same amount as Einstein’s clock A lagged behind B in accordance with his equation .5tv²/c².

This is analogous to an astronaut’s outward bound trip however, having come to a stop and adjusted his clock so that it then indicates the same time as the Earth clock (and, allowing for the fact that the Earth clock’s rate of operation is affected by it’s location in a gravitational tidal area is ticking over at the same rate as the Earth clock), the situation is precisely analogous to Einstein’s paragraph 1, chapter 4 depiction of synchronous clocks located at points A and B of K.

Having synchronized his clock with the Earth clock (having allowed for the time that it takes for light to traverse the intervening distance) the astronaut immediately accelerates and soon attains an instantaneous velocity whereby his clock is ticking over at the same rate as the (gravitationally affected) Earth clock after which his clock starts to progressively ‘go more slowly’ than the Earth clock.

Upon his arrival back at the planet he finds that his clock lags behind the Earth clock whereupon he can either conclude that his clock ‘went more slowly’ than the Earth clock during that trip or that the Earth clock ticked over at a faster rate than his own clock (i.e. the Earth clock incurred time ‘contraction’) yet, in accordance with Einstein’s 1918 article, he knows that his was the reference frame that accelerated.

As as I detailed in another posting - when Galileo wrote his book ‘Two New Sciences’ he was already in trouble with authorities so he presented it as a purely hypothetical discussion between a teacher and two of his students. Einstein also presented his 1918 article as a purely hypothetical discussion - this time between a relativist and a critic.

Having already been criticized for having stated, in his 1916 general theory, that the special theory ‘law’ of the constancy of the velocity of light required modification and, in that same year in his book ‘Relativity’ that this law was not fully valid, it was, perhaps, an attempt on his behalf to avoid further criticisms that he wrote his 1918 article in that format.

In his self-published book ‘Fiction Stranger Than Truth’ Nikolai Rudakov wrote :-

“Very few relativists have actually adopted Einstein’s explanation [of the twin paradox]. Not many authors mention the 1918 dialogue, and some who do imply that Einstein was wrong.”

The simple fact is that that when we are discussing Einstein’s concepts regarding relativity per se (not just his 1905 article) we should, I believe, refer to all of his relevant materiel including his 1918 article as well as his chapter 4 depictions and if any of it ‘argues against the validity of the mainstream understanding of relativity’ then it is Einstein who should be criticized not me! I’m just the messenger.

In my opinion Einstein’s chapter 4 can be shown to describe an out-and-return trip by an astronaut and that the ludicrous claim that the astronaut does not accept that his clock incurs time dilation but insists that the Earth clock incurs time contraction and only during his period of acceleration following turn around does not comply with (argues against) Einstein’s ‘understanding’ of relativity as presented in that chapter.

In the normal space analogy, Y and Z start at the same point in space, then both of them move through space in different paths, eventually meeting at another point in space. At that point, they find that they have accumulated different amounts of "real distance". Does this mean that the "real distance" between ticks of Y's rulers were greater?

On the assumption that Z is the astronaut - yes.

(In the first scenario you depicted A and B with B being the astronaut so I assume that when you refer to Y and Z above you are classifying Z as the astronaut.)

On the basis that the astronaut’s clock incurs time dilation (i.e. the “real time” between the ticks of Z’s clock are greater) his rule ‘must’ accordingly incur length contraction (i.e. the “real distance” between the ticks on his rule will be shorter).

Given the analogy, I suggest that if the answer is "no" for the second scenario, it must also be "no" for the first scenario. If so, then we can ask if it makes any sense to say that "time" goes more slowly for B. If it is to make sense, then "time" in that statement cannot be "real time".

My answer to both scenarios is yes.

 

[cos]

The normal space analogy takes place in normal space and time - no length contraction, no time dilation, just an analogy from everyday life.

By 'normal space analogy' I assume that you are talking about a 'real' out-and-return journey.

On the assumption that you suggest that length contraction and time dilation do not take place in reality I can only refer you to the results of the Hafele-Keating experiment as well as similar 'proofs' that time dilation does take place 'in reality'.

 

[JesseM]

have been accused of arguing the validity of the mainstream understanding of relativity however I fail to see why my referring to chapter 4 of relativity could be arguing that mainstream understanding of relativity.

It seems to me that some people are attempting to pretend that chapter 4 of special theory does not exist. If chapter 4 of relativity argues the validity of the mainstream understanding of relativity then I suggest that people should look at chapter 4. It is part and parcel of relativity thus should not be ignored even it is uncomfortable or inconvenient.

In that chapter (paragraph 1) Einstein wrote:- “If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by .5tv²/c² ... t being the time occupied in the journey from A to B.”

Nowhere in this paragraph does Einstein say that A was running slower than B as it approached it in any objective physical sense--he just says it "lags behind", meaning that the time on the A clock is less than the time on the B clock when they meet (which you would predict even if you analyzed the situation in a frame where B was running slower). I would still appreciate a basic yes/no answer to the question of whether you are arguing that A was objectively, physically ticking slower than B as A approached B. I thought you were, which was why I said your arguments conflicted with SR, but I want to be completely sure that I'm not misinterpreting you somehow.

Although Einstein made no mention of the fact - it is obvious that clock A in paragraph 1 must accelerate in order to move to B’s location. On the basis that the attainment of an instantaneous velocity can be mathematically ‘ratified’ I can only repeat Einstein’s comment that as far as the propositions of mathematics are certain, they do not refer to reality

No one denied that clock A had accelerated, I think you're misunderstanding the term "instantaneous velocity"--it does not refer to the idea of a sudden jump in velocity without smooth acceleration! "instantaneous velocity" just refers to the idea that an object has a single well-defined velocity at every instant, even if the velocity is changing continuously. For example, if the velocity of a falling object is given by the continuous function v(t) = (9.8 meters/second^2)*t, then the instantaneous velocity at the precise instant of t=2 seconds would be (9.8 meters/second^2)*(2 seconds) = 19.6 meters/second.

In any case, we are free to imagine that A accelerates for some brief time but after that it moves inertially. So my question, again, is whether during this inertial phase when A and B are approaching one another, do you think there is an objective physical truth about whether A or B is ticking slower, or do you acknowledge that different frames disagree about which is ticking slower, and in relativity no inertial frame is more "correct" than any other?

and as far as I am concerned physics should be a study of physical reality thus Einstein’s paragraph 1, chapter 4, clock A must accelerate and as Einstein showed in his 1918 Naturwissenschaften article, it is only the clock that experiences forces of acceleration (clock A) that incurs variations in it’s rates of operation not the clock referred to in his 1918 article which continues to move with uniform velocity (clock B).

I have no objection to the statement "it is only the clock that experiences forces of acceleration (clock A) that incurs variations in it's rates of operation", since every inertial frame agrees that the clock that accelerates will change its rate of ticking. The issue is just that there are perfectly valid frames where clock A was ticking slower before accelerating than it was after, so although it's an objective fact that A changed its rate of ticking, it's not an objective fact that A's rate of ticking slowed down after it accelerated. So again, I'd like to know whether you are arguing it's an objective truth that A began to run slower than B after accelerating.

Having synchronized his clock with the Earth clock (having allowed for the time that it takes for light to traverse the intervening distance)

But Einstein also points out in chapters VIII and IX here that simultaneity is relative, so two clocks that are synchronized in one frame are out-of-sync in another.

the astronaut immediately accelerates and soon attains an instantaneous velocity whereby his clock is ticking over at the same rate as the (gravitationally affected) Earth clock after which his clock starts to progressively ‘go more slowly’ than the Earth clock.

Do you argue the astronaut's clock starts to "go more slowly" in an objective physical sense, or just that it slows down in the frame of the Earth? This is the only question I'm asking for an answer to, if you don't want to address anything else in my post feel free not to.

 

[atyy]

By 'normal space analogy' I assume that you are talking about a 'real' out-and-return journey.

On the assumption that you suggest that length contraction and time dilation do not take place in reality I can only refer you to the results of the Hafele-Keating experiment as well as similar 'proofs' that time dilation does take place 'in reality'.

No. Since I am unable to communicate what I mean in the "normal space analogy", and it's clearly not being helpful, I withdraw it from discussion with apologies.

 

[cos]

If Y and Z have the same speed for the duration of their trips, and they leave and arrive together, their clocks read the same.

You previously wrote :- “Y flies from Boston directly to San Francisco. Z flies from Boston to Singapore to Japan to San Francisco.”

If “Y and Z have the same speed for the duration of their trips” but Z travels a much greater distance how can they possibly, having left together, arrive together?

A difference in clock time would imply one traveled a greater distance before reuniting...

A trip from Boston to Singapore to Japan to San Francisco IS greater than a trip from Boston to San Francisco!

...which implies a faster speed, which slows clock rate.

In my previous message I wrote:- “their clocks will be ticking over at the same rate as each other during those flights (based on v being identical)”

 

[cos]

No. Since I am unable to communicate what I mean in the "normal space analogy", and it's clearly not being helpful, I withdraw it from discussion with apologies.

That's a refreshing change from some of the messages in this thread - common courtesy. Thank you.

 

[Dale]

No. Since I am unable to communicate what I mean in the "normal space analogy", and it's clearly not being helpful, I withdraw it from discussion with apologies.

Hi atyy, don't give up quite yet.

How about instead of this:

In the normal space analogy, Y and Z start at the same point in space, then both of them move through space in different paths, eventually meeting at another point in space. At that point, they find that they have accumulated different amounts of "real distance". Does this mean that the "real distance" between ticks of Y's rulers were greater?

We change it to:

Drivers Y and Z head north from Columbia, SC and eventually meet in Charleston, WV. Driver Y goes through Charlotte, NC and his odometer records 356 miles for the trip. Driver Z goes through Nashville, TN and his odometer records 834 miles for the trip. Does this mean that the real distance between ticks of Y's odometer were 2.3 times greater?

I hope that captures your meaning in a more accessible manner.

 

[atyy]

I hope that captures your meaning in a more accessible manner.

Your version captures my meaning exactly. Thanks!

 

[Dale]

Hi cos,

As you consider the revised example, please remember that atyy is talking only about spatial distances, not time. So the duration and speed of the respective trips are explicitly not considered. This is purely a geometrical question.

Do you think that the distance between the ticks of Y's odometer was 2.3 times greater than the distance between the ticks of Z's odometer?

 

[phyti]

The muons have a slowed rate of decay in our frame where they are moving at relativistic speed, but they aren't slowed down in any objective, frame-independent sense. You can analyze the behavior of muons perfectly well in a frame where the muons are at rest and the Earth is moving at relativistic speed, and you get the exact same prediction about the point on Earth where they decay.

The objective is not to analyze them in another frame. It's to compare the lifetime of the moving group to that of a second group in the lab. The same frame, same observers, the only factor changed is the speed of the group. It's called a controlled experiment. The behavoir of the particles changes as a result of speed. Is that not objective?

If you don't understand that any situation in special relativity can be analyzed in any inertial frame using precisely the same laws of physics (so in each frame you assume clocks moving faster in that frame are slowed down by a greater amount) and you'll always get all the same predictions about local physical events (like whether a muon reaches the surface, or what two clocks read at the moment they pass next to each other), you've missed one of the most central conceptual ideas of SR--this is the meaning of the first postulate.

Perhaps this presumptive attitude is why some don't respond to you posts.

 

[JesseM]

The objective is not to analyze them in another frame. It's to compare the lifetime of the moving group to that of a second group in the lab. The same frame, same observers, the only factor changed is the speed of the group. It's called a controlled experiment. The behavoir of the particles changes as a result of speed. Is that not objective?

If you're only analyzing them in one frame, then this has nothing to do with the question of which group of muons is "actually, physically" aging slower. It's certainly true that in the lab frame, group A of muons at rest in this frame will decay at an earlier time than the group B of muons moving at relativistic speed in the lab frame. On the other hand, in the rest frame of group B, the group B muons decay at an earlier time than the group A muons. Both frames make exactly the same predictions about physical events like what position on Earth the muons will decay and what the local Earth-clocks at that position will read when they decay.

If you don't understand that any situation in special relativity can be analyzed in any inertial frame using precisely the same laws of physics (so in each frame you assume clocks moving faster in that frame are slowed down by a greater amount) and you'll always get all the same predictions about local physical events (like whether a muon reaches the surface, or what two clocks read at the moment they pass next to each other), you've missed one of the most central conceptual ideas of SR--this is the meaning of the first postulate.

Perhaps this presumptive attitude is why some don't respond to you posts.

I said if you don't understand, which leaves open the possibility that you do understand, if you do just say so. But our discussion started when you seemed to call into question my statement "As I said, this claim that any clock is 'actually, physically' going more slowly than another contradicts relativity" when you asked "Then what was measured in the prolonged half life of muons?" (and in a later post you also called into question another accepted feature of SR, length contraction) Do you agree that which group of muons decays faster depends on which frame you use, and that all inertial frames are equally valid in SR and all make the same predictions about the results of empirical measurements, so there can be no basis in relativity for saying that either group of muons "actually, physically" decayed more slowly?

 

[phyti]

cos;
from post 110

In that chapter (paragraph 1) Einstein wrote:- “If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by .5tv2/c2 ... t being the time occupied in the journey from A to B.”

In paragraph 3 Einstein refers to a clock that has remained at rest compared with an identical clock that has moved in a closed curve around that clock. I am of the opinion that he implied that clock B in paragraph 1 remains at rest ergo, in that chapter, Einstein does not allow that clock B “moves through spacetime”.

If someone were to draw a diagram of clocks A and B moving through spacetime they would be presenting that phenomenon from the point of view of another reference frame however Einstein specifically pointed out that the event is “viewed in the stationary system” (i.e. clock B’s reference frame).

Here is a space-time diagram from the B-frame.

Here is a quote from the Max Born book, page 257, which you have (A and B swapped).

"The paradoxical feature of this result lies in the circumstance that every internal process in the system A must take place more slowly than the same process in the system B."

Because A & B are synchonized initially, the only change is the motion of A. If Albert states there is a time difference when they meet, the time effect must be caused by the motion. He authored the theory, so he should know.

For those who do not understand, just because we can find a reference frame with a different perspective, does not mean this case is less real.

 

[JesseM]

cos;
from post 110Here is a space-time diagram from the B-frame.

Here is a quote from the Max Born book, page 257, which you have (A and B swapped).

"The paradoxical feature of this result lies in the circumstance that every internal process in the system A must take place more slowly than the same process in the system B."

I'd like to see the context of that quote, I wonder if Born specified that he was talking about what was happening in the rest frame of A. Looking at some other sample pages from the google book preview, I note that on p. 255 Born writes:

The same remarks apply to the relativity of time. An ideal clock has always one and the same rate of beating in the system of reference in which it is at rest. It indicates the "proper time" of the system of reference. Regarded from another system, however, it goes more slowly. In such a system a definite interval of the proper time seems longer. Here, too, it is meaningless to ask what is the "real" duration of an event.

Because A & B are synchonized initially,

Only relative to the time coordinates of the frame where they are initially at rest.

the only change is the motion of A. If Albert states there is a time difference when they meet, the time effect must be caused by the motion. He authored the theory, so he should know.

For those who do not understand, just because we can find a reference frame with a different perspective, does not mean this case is less real.

I didn't say any frame's perspective was "less real" than any others, just that no frame's perspective is more "physical" than any other's, so if different frames disagree about some question there can be no singe "true" physical answer to that question. Of course it is valid to say that in the rest frame of B, A is running slower than B after A accelerates...but do you claim that in this scenario A is "actually, physically" running slower than B as they approach one another?

 

[atyy]

"The paradoxical feature of this result lies in the circumstance that every internal process in the system A must take place more slowly than the same process in the system B."

Because A & B are synchonized initially, the only change is the motion of A. If Albert states there is a time difference when they meet, the time effect must be caused by the motion. He authored the theory, so he should know.

For those who do not understand, just because we can find a reference frame with a different perspective, does not mean this case is less real.

Time dilation and length contraction are said to be "real" by many standard books (Born is hardly the only one). On the other hand, it is also said that the only "real" things are frame independent quantities. I suspect it is two definitions of "real" here.

We could try "fast moving muons really decay more slowly, but they are not really moving fast". If the second half of that statement makes sense, then the first half cannot make sense. So maybe we try,"If a muon is found to be moving fast, it will decay more slowly", which makes perfect sense since the conditional is equivalent to specifying a reference frame. Born has a similar conditional "if the clocks are synchronized", which is again equivalent to a choice of reference frame. So if we define "velocity" or "synchronization" to be "real", then time dilation automatically becomes real.

It seems that the twin paradox can be stated with or without an initial synchronization. This is because there is no need to define simultaneity to mark the start and end of the story (unlike Einstein's Chap 4 or Born's clock, which requires a definition of simultaneity to mark the start of the story). Regardless of initial synchronization, the difference in accumulated proper time is real in an observer independent sense. Yet, the relative rate of their ageing is not real in an observer independent sense, since like velocity, the relative rate of ageing cannot even make sense without a definition of simultaneity, which is the choice of a reference frame. Does this make any sense?

 

[cos]

As you consider the revised example, please remember that atyy is talking only about spatial distances, not time. So the duration and speed of the respective trips are explicitly not considered. This is purely a geometrical question.

Do you think that the distance between the ticks of Y's odometer was 2.3 times greater than the distance between the ticks of Z's odometer?

I’m having trouble getting my head around that depiction (I assume that it has some relationship to length contraction however on the basis that length contraction is ‘determined’ on the basis of relative speeds and, as you point out, the speeds of the respective trips are not taken into account) but - no - I do not think that the distance between the ticks of Y's odometer was 2.3 times greater than the distance between the ticks of Z's odometer.

The distance between the respective ‘ticks’ on both odometers is determined on the basis of the physical distance traveled by their vehicles i.e. on the number of rotations of their wheels due to their contact with the road and because the respective lengths of the amount of road traversed varies they attain different odometer readings.

If, in lieu of a direct trip home after turn-around, the astronaut takes a diversionary trip to Mars (off to one side of the direct route) but at the same speed as he would have been moving on his direct trip he will calculate that the distance he travels is greater than it would have been for the direct trip.

His ‘odometer’ will record more ticks on the stop-Mars-home journey than it would have for the direct trip however this does not mean that the distance between those ticks varies depending on which route he takes but merely that there are more of them as a result of the longer distance traveled on the stop-Mars-home journey than there would have been on the direct trip.

I’m sorry, but the answer to your question seems so obvious that perhaps I misinterpreted it.

 

[atyy]

Yet, the relative rate of their ageing is not real in an observer independent sense, since like velocity, the relative rate of ageing cannot even make sense without a definition of simultaneity, which is the choice of a reference frame. Does this make any sense?

Are there are cases where the relative rate of ageing makes sense in an observer independent way, but the accumulated proper time is observer dependent? How about two clocks which are stationary relative to each other in some inertial frame, but separated by some distance. Is it the case that their relative rates will be the same in all frames, but the elapsed proper time is frame dependent?

 

[atyy]

I do not think that the distance between the ticks of Y's odometer was 2.3 times greater than the distance between the ticks of Z's odometer.

Yes, that's what I also thought the answer should be. I'll let DaleSpam have the extended commentary since it was his version that clarified things nicely.

 

[cos]

Here is a quote from the Max Born book, page 257, which you have (A and B swapped).

"The paradoxical feature of this result lies in the circumstance that every internal process in the system A must take place more slowly than the same process in the system B."

Because A & B are synchronized initially, the only change is the motion of A. If Albert states there is a time difference when they meet, the time effect must be caused by the motion. He authored the theory, so he should know.

Thank’s for that support of my argument.

It was perhaps about 18 years ago that I read Born’s book in its entirety and it would have been then that I placed a bookmark in same which, to my surprize, now, I found to be located between pages 254 and 255.

To my shame I now find that my criticism of Born for depicting a sliced cucumber as an analogy for length contraction was (ignorantly, on my behalf) taken out of context thus was totally unwarranted.

Toward the conclusion of the previous paragraph (the penultimate sentence of same) on page 254 Born wrote:-

“Thus the contraction is only a consequence of our way of regarding things and is not a change of a physical reality.”

However, on page 255, he wrote:-

“In exactly the same way a rod in Einstein’s theory has various lengths according to the point of view of the observer. One of these lengths, the statical or proper length, is the greatest but this does not make it more real than the others.”

It seems, to me, that this comment conflicts with his abovementioned ensuing comment that an observation that a moving rod appears to contract in length “...is only a consequence of our way of regarding things and is not a change of a physical reality.”

(ref: my comment below in relation to my understanding of ‘reality’).

For those who do not understand, just because we can find a reference frame with a different perspective, does not mean this case is less real.

My interpretation of ‘reality’ is in relation to an event that takes place in an observer’s reference frame.

An observer in another reference frame may well have a different opinion of what is taking place in the first reference frame however I believe that he should be allowed to conclude that what appears to be taking place in the other reference frame is affected by their respective rates of travel.

Thus what appears to that observer to be taking place in another reference frame is only a consequence of his way of regarding things and is not a change of a physical reality in that other reference frame.

In his book ‘An Introduction to the Special Theory of Relativity’ Professor Robert Katz wrote:-

“Is the moving rod really contracted in its direction of motion? Is time really dilated? These questions depend on what is meant by really. In physics what is real is identical with what is measured.”

In the preceding paragraph Katz wrote:-

“The way in which we set up to measure the length of a moving rod determines that we will measure a shorter length than the rod length.”

This gives me the impression that we could set up an experiment in such a way that we would not measure a shorter length than the rod length.

On the basis that ‘in physics what is real is identical with what is measured’ and, having set up the experiment in a different way, we measure the same (or even a greater) length than the rod length then that determination should be accepted as being reality - according to Katz.

When Albert Einstein wrote in the introduction to his general theory of relativity that the law of the constancy of the velocity of light ‘requires modification’ or in his book ‘Relativity’ that this law is not fully valid he was, apparently, castigated by his colleagues (particularly Max Abrahams) for ‘arguing against the validity of the [then] mainstream understanding of relativity’ however I believe that he had every right to do so!

If Einstein (or Max Born et al) were to have made a comment which, posted in this group, ‘argued against the validity of the mainstream understanding of relativity’ would it be censored?

When Einstein’s OEMB was published he was castigated by his colleagues for arguing against the validity of the mainstream understanding of Newtonian physics.

If anyone had been successful in having Einstein’s theory (or those of Lorentz and Fitzgerald et al) banned from dissemination we may not, now, be having these exchanges of opinions.

 

[JesseM]

My interpretation of ‘reality’ is in relation to an event that takes place in an observer’s reference frame.

So does that mean in your way of speaking, you allow different observers to have different "realities"? A reference frame is really just a coordinate system--even two observers at rest relative to one another may choose to place the origin of their coordinate systems in different places, and thus have different answers to the question of the x-coordinate assigned to a certain event, say. Would you say that for one observer, the "reality" is that the event occurred at x=6 meters and for another the "reality" is that it occurred at x=10 meters, simply because they choose to position the origins of their system differently? I would say that coordinate assignments are a matter of convention, not reality, and I think most physicists would speak the same way (I have seen many physicists talk about the 'simultaneity convention' of a particular coordinate system, for example), and would interpret a phrase like "objective truth" or "physical reality" in the context of relativity to mean a coordinate-invariant truth (see the discussion of the 'mainstream interpretation' of relativity on pages 22-25 here).

If Einstein (or Max Born et al) were to have made a comment which, posted in this group, ‘argued against the validity of the mainstream understanding of relativity’ would it be censored?

But as you said earlier, other statements of theirs make clear they agree there is no single absolute truth about the rate a clock is ticking. If someone comes to this group and posts an ambiguous comment, I'd ask for clarification about what they were saying. But you do not seem willing to answer my basic question about your argument, the same one I just asked phyti, concerning the thought-experiment in section 4 of Einstein's paper: do you claim that in this scenario A is "actually, physically" running slower than B as they approach one another?

Are you not answering me because you're ignoring me as some sort of "punishment" (note that this is a public forum rather than a private discussion, so I continue to respond to your posts in part so they don't mislead other readers), or do you not have a clear answer to this question in your own mind? If the issue is that you define words like "actually, physically" in a way that allows there to be multiple equally valid truths about what is "actually, physically" occurring, then as I said I think this would differ from the way virtually all physicists would use this type of language, but you are free to use these words any way you want, all you would need to do is clarify that you do define them such that there can be multiple equally valid truths and I would no longer see your posts as misleading.

 

[Dale]

I’m having trouble getting my head around that depiction (I assume that it has some relationship to length contraction however on the basis that length contraction is ‘determined’ on the basis of relative speeds and, as you point out, the speeds of the respective trips are not taken into account) but - no - I do not think that the distance between the ticks of Y's odometer was 2.3 times greater than the distance between the ticks of Z's odometer.

The distance between the respective ‘ticks’ on both odometers is determined on the basis of the physical distance traveled by their vehicles i.e. on the number of rotations of their wheels due to their contact with the road and because the respective lengths of the amount of road traversed varies they attain different odometer readings.

If, in lieu of a direct trip home after turn-around, the astronaut takes a diversionary trip to Mars (off to one side of the direct route) but at the same speed as he would have been moving on his direct trip he will calculate that the distance he travels is greater than it would have been for the direct trip.

His ‘odometer’ will record more ticks on the stop-Mars-home journey than it would have for the direct trip however this does not mean that the distance between those ticks varies depending on which route he takes but merely that there are more of them as a result of the longer distance traveled on the stop-Mars-home journey than there would have been on the direct trip.

I’m sorry, but the answer to your question seems so obvious that perhaps I misinterpreted it.

No, you didn't misinterpret it. It is obvious when we are dealing with space and normal Euclidean geometry. We have a very visceral understanding of geometric concepts like distance along a path, and we intuitively know that different paths through the same two points can have different lengths without paradox. We clearly understand that this difference in length is a geometric property of the paths themselves, not the odometers.

Now, special relativity can be most conveniently formulated mathematically using Minkowski geometry with one timelike dimension and three spacelike dimensions. Minkowski geometry is very analogous to the normal Euclidean geometry that we are so comfortable with. The only major difference is that distances are called intervals and are given by ds²=-dt²+dx²+dy²+dz².

In the Minkowski geometric formulation of special relativity a clock is nothing more than an odometer for measuring the interval along a timelike path (e.g. a clock measures one year per light-year). In this formulation, the time dilation and all other SR effects are immediately seen to be no more surprising or paradoxical than the different distances traveled by drivers Y and Z. In Minkowski spacetime clocks don't slow down in any physical sense, they simply take a different path through spacetime and the different interval is a property of that path rather than a property of the clock that measures that path.

 

[cos]

Are you not answering me because you're ignoring me...

You threatened to report me to the group moderators for having the temerity to express my opinions so irrespective of your repetitive taunts I see no point in providing you with potential ammunition.

----> CORRESPONDENCE TERMINATED <-----

 

[JesseM]

You threatened to report me to the group moderators for having the temerity to express my opinions so irrespective of your repetitive taunts I see no point in providing you with potential ammunition.

They are not "taunts", they are questions about what you are trying to argue. The point is that I don't know if your opinions actually are in conflict with SR because you aren't willing to answer these questions. As I said in my previous post, if you wish to clarify that when you said one clock was "actually, physically" running slower than the other, you did not mean this in the exclusive sense I had originally interpreted it (so that you allow for different observers to disagree about which of two clocks is 'actually, physically' running slower and do not claim that one observer is more correct than the other), then I would withdraw my objection that your statements conflict with relativity. On the other hand, if you think that there is a single, exclusive truth about which of two clocks is running slower, this does conflict with relativity, but if you said so I would not report you to the moderators if you were willing to engage in rational discussion about it. The stated purpose of this forum is to help people understand mainstream SR rather than to advocate alternative ideas, and I hope you respect that (there are plenty of other forums one can go to try to shoot down SR); but there is some leeway in that if people have doubts about some aspect of mainstream SR but are genuinely interested in discussing how advocates of the mainstream view would account for whatever seeming problems they have, rather than simply wanting to post polemics against the mainstream view, then I think that isn't a clear violation of the rules.

 

[cos]

In Minkowski spacetime clocks don't slow down in any physical sense, they simply take a different path through spacetime and the different interval is a property of that path rather than a property of the clock that measures that path.

My posting is not in relation to Minkowski spacetime but to Einstein's chapter 4 OEMB depiction wherein he wrote that a balance clock at the equator 'must go more slowly' than a similar clock at one of the poles.

It seems to me that although "In Minkowski spacetime clocks don't slow down in any physical sense..." equatorial clocks do, according to Einstein "go more slowly" than polar clocks.

 

[JesseM]

My posting is not in relation to Minkowski spacetime but to Einstein's chapter 4 OEMB depiction wherein he wrote that a balance clock at the equator 'must go more slowly' than a similar clock at one of the poles.

Minkowski spacetime just means that there is no spacetime curvature, it doesn't say anything about the shape of the paths. So, if you have a clock at the equator of a massless rotating sphere, you're still dealing with a situation in Minkowski spacetime, it's only if you assume the sphere's mass is curving spacetime (which Einstein wouldn't have been assuming in the 1905 paper since GR hadn't been invented) that you're no longer in Minkowski spacetime.

It seems to me that although "In Minkowski spacetime clocks don't slow down in any physical sense..." equatorial clocks do, according to Einstein "go more slowly" than polar clocks.

The odometer analogy works in this case too. In spacetime, the worldline of the clock on the equator would look like a type of helix, as depicted in this diagram with the number of spatial dimensions reduced to 2, and the worldline of the clock at the pole would be a straight path through spacetime going through the center of the helix. So if we instead imagine submarines moving through a 3D volume of water, one going in a straight line and the other taking a helix-shaped path through space that wraps around the straight line, then if each submarine has some type of 3D odometer keeping track of the mileage of its path through the water, of course the helix-shaped path will accumulate greater mileage, but that's a function of the shape of its path through space rather than indicating its miles are a different length than the miles of the submarine going along a straight path.

 

[Dale]

My posting is not in relation to Minkowski spacetime but to Einstein's chapter 4 OEMB depiction wherein he wrote that a balance clock at the equator 'must go more slowly' than a similar clock at one of the poles.

It seems to me that although "In Minkowski spacetime clocks don't slow down in any physical sense..." equatorial clocks do, according to Einstein "go more slowly" than polar clocks.

One particular section of one particular work is a rather narrow focus. I am trying to provide you with a much more general conceptual tool.

In addition to being more intuitive than other approaches, the spacetime geometric approach is universally applicable. It applies equally well for any arbitrary set of clocks traveling on any arbitrary set of paths. Once you have the appropriate metric for a given coordinate system it even applies in non-Cartesian cases and in the curved spacetimes of general relativity. In short, it always works.

JesseM gave a brief description of how the geometric approach would work for the polar/equatorial case. If you have any questions I would be glad to address them.

 

[phyti]

I'd like to see the context of that quote, I wonder if Born specified that he was talking about what was happening in the rest frame of A. Looking at some other sample pages from the google book preview, I note that on p. 255 Born writes:


Only relative to the time coordinates of the frame where they are initially at rest.

I didn't say any frame's perspective was "less real" than any others, just that no frame's perspective is more "physical" than any other's, so if different frames disagree about some question there can be no singe "true" physical answer to that question. Of course it is valid to say that in the rest frame of B, A is running slower than B after A accelerates...but do you claim that in this scenario A is "actually, physically" running slower than B as they approach one another?

Einstein states when the clocks are togther, A lags behind B. The began in synch. Only B moved. The trip is over. How did the A clock get behind the B clock, without slowing down?
We are not talking Harry Potter physics!

 

[phyti]

to cos; post 127

It seems, to me, that this comment conflicts with his abovementioned ensuing
comment that an observation that a moving rod appears to contract in length
“...is only a consequence of our way of regarding things and is not a change
of a physical reality.”

He is talking about physical events and perception of the events, and assumes the reader can tell the difference from the context. He is saying time dilation is real/physical, an altered state of the moving system, and length contraction is a measurement/perception process. A biological system is just atoms and photon exchanges, thus the astronaut does not perceive the time dilation effect, he is part of it. The measurement process involves two spatial endpoints of an object, but each signal originated at a different time.
You are probably aware that some authors know the subject, but are not adept at communicating ideas, i.e., cucumbers.

My interpretation of ‘reality’ is in relation to an event that takes place in
an observer’s reference frame.

Your reality then is perception, which is sufficient for everyday life, unless you are an astronaut!

The saying 'things are not as they appear', requires a distinction between events (reality) and perception (awareness of events).
Subjective simultaneity is a sphere of light containing a composition of signals from various parts of the universe, converging on the viewer. I doubt you would conclude that a distant event happened simultaneously with something happening next to you, even though the light signals are coincident. Perception is 'now', events are always in the past.

I do not agree with Robert Katz. Suppose upon measuring a fast moving space probe from earth, you accept your length measurement of 20 ft. as 'real'. You build a 21 ft container for it, send it on a shuttle with meets the probe in orbit, and find it's really 24ft.
Which is real? Again, perception or reality?

If Einstein (or Max Born et al) were to have made a comment which, posted in
this group, ‘argued against the validity of the mainstream understanding of
relativity’ would it be censored?

Most people don't like change, in any aspect of life unless there is an immediately obvious benefit. Otherwise they have to learn new things and readjust their thinking.
Sometimes it's plain ignorance, eg., the LHC experiments at CERN. We could go way back, when it was blasphemy to suggest the Earth was not the center of the ego-centric universe. History is full of this.

Thanks for a sensible discussion.

 

[JesseM]

Einstein states when the clocks are togther, A lags behind B. The began in synch. Only B moved. The trip is over. How did the A clock get behind the B clock, without slowing down?
We are not talking Harry Potter physics!

Einstein only says they "began in sync" in the frame where B is at rest (his words are 'If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous'). Do you understand that because of the relativity of simultaneity, if we choose a different inertial frame where A is at rest after it accelerates, the two clocks were not in syc to begin with in this frame, instead B was already significantly ahead of A at the moment before A accelerated? So, even though B was running slower than A after A accelerated, B is still ahead when A reaches it because of this "head start". This follows directly from the Lorentz transformation, and I gave a numerical example and showed how the numbers work out in post #31 of this thread.

 

[Dale]

Einstein states when the clocks are togther, A lags behind B. The began in synch. Only B moved. The trip is over. How did the A clock get behind the B clock, without slowing down?

By taking a longer path through spacetime.

 

[JesseM]

By taking a longer path through spacetime.

In this case Einstein was talking about two clocks that started out a certain distance apart, rather than a twin paradox scenario where they start and finish at the same position, so I don't know if this answer is applicable...you'd have to pick points on each clock's worldline to be the "starting points" of each clock's path through spacetime (the ending point being when they meet of course), but the choice is somewhat arbitrary, and which one has a longer path through spacetime depends on what starting points you choose.

edit: I suppose you might have meant something like "longer path through spacetime from the moment each clock was set to zero to the moment they met", in which case your statement would make sense since they'd been synchronized in B's rest frame before A accelerated.

 

[Fredrik]

Einstein states when the clocks are togther, A lags behind B. The began in synch. Only B moved. The trip is over. How did the A clock get behind the B clock, without slowing down?

(I wrote this before JM and DS posted their replies).

I think the point was that a statement like "A is actually, physically running slower than B" doesn't make sense, not that it's wrong. The "actually, physically" only makes sense if we're talking about proper time, which is coordinate independent and only defined along a path. The "running slower" only makes sense if we specify one specific event on each of the world lines, and use the co-moving inertial frames (or two other coordinate systems which we must specify) to compare the clocks' ticking rates in those two frames, at those two events.

A doesn't "slow down". Both A and B do what they're supposed to, which is to measure a property of their respective world lines. It's the world lines that are different, not the clocks.